Question

Four point charges have the same magnitude of 2.0 ×
10^{-12} C and are fixed to the corners of a square that is
2.8 cm on a side. Three of the charges are positive and one is
negative. Determine the magnitude of the net electric field that
exists at the center of the square.

Answer #1

The trick for this problem is to recognize that, at the center of
the square, the two +ve charges across from each other cancel out.
You only need to consider the negative charge (field flows toward)
and the charge across from it (field flows away).

The distance from the center to a corner is

d = 0.028m / √2 = 0.0197 m, so the field at the center due to the
negative charge is

E = 8.99e9 N·m²/C² * 2.0 e-12C / (0.0197m)² = 46.32 N/C

toward the charge.

For the positive charge across from it, the magnitude of the field
must be the same, but it too flows toward the negative
charge.

Therefore the net field at the center is

E = 92.64 N/C toward the negative charge.

Four point charges are located at the corners of a square. Each
charge has magnitude 1.70 nC and the square has sides of length
2.40 cm. Find the magnitude of the electric field (in N/C) at the
center of the square if all of the charges are positive and three
of the charges are positive and one is negative.
HINT
(a)
all the charges are positive
N/C
(b)
three of the charges are positive and one is negative

Four point charges are located at the corners of a square. Each
charge has magnitude 3.50 nC and the square has sides of length
3.20 cm. Find the magnitude of the electric field (in N/C) at the
center of the square if all of the charges are positive and three
of the charges are positive and one is negative.
(a) all the charges are positive N/C
(b) three of the charges are positive and one is negative
N/C

Three equal positive point charges of magnitude Q = 9.00μ C are
located at three corners of a square of edge length d = 8.1 cm. A
negative charge -27.00μ C is placed on the fourth corner. At the
position of the negative charge, what is the magnitude of the
electric field due to the three positive charges?
What is the magnitude of the attractive force on the negative
charge?

Four +10 µC point charges are at the corners of a square of side
11 m. Find the potential at the center of the square (relative to
zero potential at infinity) for each of the following
conditions.
(a) All the charges are positive
kV
(b) Three of the charges are positive and one is negative
kV
(c) Two are positive and two are negative
kV

There are four charges, each with a magnitude of 1.91 μC. Two
are positive and two are negative. The charges are fixed to the
corners of a 0.266-m square, one to a corner, in such a way that
the net force on any charge is directed toward the center of the
square. Calculate the magnitude of the net electrostatic force
experienced by any charge.

There are four charges, each with a magnitude of 2.18 µC. Two
are positive and two are negative. The charges are fixed to the
corners of a 0.21-m square, one to a corner, in such a way that the
net force on any charge is directed toward the center of the
square. Find the magnitude of the net electrostatic force
experienced by any charge.

Four point charges are located at the corners of a square, 2.0 m
by 2.0 m. On each of two diagonally opposite corners are 2.0 μC
charges. On each of the other two corners are -2.0 μC charges. What
is the direction and magnitude of the force on each charge?

Four point charges are located on the corners of the square with
the side of 40cm. Three charges are 1 μC and one is -1 μ C. Find
the electric potential at the center of the square (Assume that the
potential at infinity is zero)

Three +3.0 μC point charges are at the three corners of a square
of side 0.50 m. The remaining corner is occupied by a negative -3.0
μC charge. Find the magnitude of the electric field at the center
of the square. (k = 1/4πε0 = 8.99 × 109 N ∙
m2/C2)

Identical point charges of +1.2 µC are fixed to three
of the four corners of a square. What is the magnitude |q| of the
negative point charge that must be fixed to the fourth corner, so
that the charge at the diagonally opposite corner experiences a net
force of zero?
|q| = Number _______ Units _____

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